Problem: Mika can eat $21$ hot dogs in $6$ minutes. She wants to know how many minutes $(m)$ it would take her to eat $35$ hot dogs if she can keep up the same pace. How many minutes would Mika need to eat $35$ hot dogs?
Explanation: We're dealing with a proportional relationship, so each ratio of hot dogs to minutes must be equivalent. Here's one way to write the proportion: $\dfrac{21 \text{ hot dogs}}{6\text{ mins}} = \dfrac{35\text{ hot dogs}}{m\text{ mins}}$ Let's solve for $m$ : $\dfrac{21 \text{ hot dogs}}{6\text{ mins}} = \dfrac{35\text{ hot dogs}}{m\text{ mins}}$ $m \cdot 21 = 35 \cdot 6 $ $21m = 210$ $m = \dfrac{210}{21}~~~~~~~~~~~$ Divide both sides by $21$. $m = 10$ Mika would need $10$ minutes to eat $35$ hot dogs.